However, bookmakers aren't ruling out a Celtic stay for the 24-year-old Dutchman, who could yet be tempted to stay with the Bhoys should they make the Champions League group stages.
The rest come in at prices of 6/1 or higher, with Van Dijk 7/2 to remain with Celtic.
That suggests a straightforward choice between joining Southampton and staying with Celtic is likely for the 24-year-old, with Everton in with a slightly lower chance of prising him to Goodison Park.
Both the Toffees and the South Coast side are in need of a new defender but neither club can offer Van Dijk Champions League football.
It will be interesting to see just how much the odds shift once Celtic get through their play-off against Malmo. Should they make the group stages, Parkhead will become a much likelier destination for the Dutchman, although anything less could see Southampton and Everton's odds shorten considerably.